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We study the existence and multiplicity of solutions and the global solutioncurve of the following free boundary value problem, arising in plasma physics,see R. Temam [18], and H. Berestycki and H. Brezis [3]: find a function $u(x)$and a constant $b$, satisfying \[ \Delta u+g(x,u)=p(x) \;\; \mbox{in $D$} \] \[  u \,| \, _{\partial D}=b, \;\;\;\; \int_{\partial D} \frac{\partialu}{\partial n} \, ds=0 \,. \] Here $D \subset R^n$, is a bounded domain, with asmooth boundary. This problem can be seen as a PDE generalization of theperiodic problem for one-dimensional pendulum-like equations. We usecontinuation techniques. Our approach is suitable for numerical computations.

A global solution curve for a class of free boundary value problems arising in plasma physics